Numerical solution of simultaneous first order ODES Application of Complex Variables But the differential equations arising out of many physical problems do not belong to a specific form and some times analytical solution may not even exist. In some cases it may be very difficult tosolve by analytical methods.
In such cases Numerical Methods assumes importance and computers help in many numerical methods for obtaining the result to the highest degree of accuracy. We discuss several numerical methods for solving an initial value problem. Then wecan find the value of y for various values of x in theneighbouthood of x. Find y. To find y 0. Substituting these values in 1 for computing y 4. We have to first find y 0. Also find y O. Thus 0. Using Taylor's.
Computey 0. Compute 0,03 using the expansion of y upto second degree terms. Computey 1. Find the third order approximation of the solution and use it to compute y 1. Solution By modified By analytical u x Euler's method method y 1. Using modified Euler's method find y 0. It may be noted that lesser is the step size, greater is the accuracy. Related searches M4 textbook. Documents Similar To M4 textbook by dr ksc.
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